Interferometers which superimpose two versions of the same optical wavefront are known as shearing interferometers. Using a shearing interferometer one may measure the relative phase between different points on the same wavefront. Shearing interferometers have been employed for component testing, astronomical observation, turbulence studies, coherence measurement, and optical signal processing. They are classed as lateral, radial, reversing, or rotational, depending on whether the resulting wavefront versions are related to each other by translation, dilation, reflection about a line, or rotation, respectively.
The problem addressed by my invention is to operate on an object which is one-dimensional and to provide simultaneous interference between every pair of points on the object. Specifically, suppose that the object has scalar field amplitude EQU .alpha.(x,y,t)=a(x,t).delta.(y), EQU where .delta. is the Dirac delta function and a(x,t) is some function to be examined. The problem is to produce a plane in which the optical intensity has a term proportional either to EQU I.sub.1 (x,y,t)=Re{a(x,t-d)a*(y,t-d)} EQU or to EQU I.sub.2 (x,y,t)=Re{a(x,t-d)a*(x+y,t-d)},
depending upon which format is more convenient for the application, and where d is some delay. (For the remainder of this disclosure, the understood time dependence will be suppressed.)
Viewing a as a vector indexed by x, the result I.sub.1 may be regarded as (the real part of) the outer product of a with itself, that is, I.sub.1 is a matrix whose entries are all the possible products of one element of a with another element of a. The result I.sub.2 contains the same information in a different format. The former description provides coordinates which explicitly index the two factors, while the latter format gives one coordinate which is the difference between the indices of a.